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The Gauss map on a class of interval translation mappings [PDF]
Israel Journal of Mathematics, 2002 We study the dynamics of a class of interval translation map on three intervals. We show that in this class the typical ITM is of finite type (reduce to an interval exchange transformation) and that the complement contains a Cantor set. We relate our maps to substitution subshifts.
Henk Bruin, Serge Troubetzkoy
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On the Gauss maps of singular projective varieties [PDF]
Journal of the Australian Mathematical Society, 2002 AbstractHere we study the dimension δ(m, X) of the general fibers of the m-Gaussian map of a singular n-dimensional variety X ⊂ Pn. We show that for all integers a, b, c, d with n ≦ a < b ≦ c < d ≦ N − 1 and a + d = b + c we have δ (a, X) + δ(d, X) > δ(b, X) + δ(c, X).
Edoardo Ballico
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Surfaces with $1$-type Gauss map [PDF]
Kodai Mathematical Journal, 1996 The author proves the following theorem. Let \(M\) be an orientable connected surface of Euclidean 3-space \(E^3\). Then \(M\) has 1-type Gauss map if and only if \(M\) is an open part of a sphere or an open part of a circular cylinder. Reviewer's remark: Compact submanifolds of Euclidean spaces with 1-type Gauss map were completely classified in ...
Chang-Rim Jang
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HYPERSURFACES WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
Taiwanese Journal of Mathematics, 2007 Uğur Dursun
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Pacific Journal of Mathematics, 1989 A construction is given whereby a Riemannian manifold induces a Riemannian metric on the total space of a large class of fibre bundles over it. Using this metric on the appropriate bundles, necessary and sufficient conditions are given for the Gauss map and the spherical Gauss map to be harmonic.
Jensen, Gary R., Rigoli, Marco
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SUBMANIFOLDS WITH BIHARMONIC GAUSS MAP [PDF]
International Journal of Mathematics, 2010 We generalize the Ruh–Vilms problem by characterizing the submanifolds in Euclidean spaces with proper biharmonic Gauss map and we construct examples of such hypersurfaces.
BALMUS A, MONTALDO, STEFANO, ONICIUC C.
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On Separable Higher Gauss Maps [PDF]
Michigan Mathematical Journal, 2019 We study the $m$-th Gauss map in the sense of F.~L.~Zak of a projective variety $X \subset \mathbb{P}^N$ over an algebraically closed field in any characteristic. For all integer $m$ with $n:=\dim(X) \leq m < N$, we show that the contact locus on $X$ of a general tangent $m$-plane is a linear variety if the $m$-th Gauss map is separable.
Furukawa, Katsuhisa, Ito, Atsushi
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The Gauss map of minimal surfaces in the Heisenberg group [PDF]
, 2010 We study the Gauss map of minimal surfaces in the Heisenberg group $\mathrm{Nil}_3$ endowed with a left-invariant Riemannian metric. We prove that the Gauss map of a nowhere vertical minimal surface is harmonic into the hyperbolic plane $\mathbb{H}^2 ...
Daniel, Benoît
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On the Gauss map of ruled surfaces [PDF]
Glasgow Mathematical Journal, 1992 Let M2 be a (connected) surface in Euclidean 3-space E3, and let G:M2→S2(1) ⊂ E3 be its Gauss map. Then, according to a theorem of E. A. Ruh and J. Vilms [3], M2 is a surface of constant mean curvature if and only if, as a map from M2 to S2(1), G is harmonic, or equivalently, if and only ifwhere δ is the Laplace operator on M2 corresponding to the ...
Baikoussis, C., Blair, D. E.
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